A rectangular billboard 7 feet in height stands in a field so that its bottom is 12 feet above the ground. A nearsighted cow with eye level at 4 feet above the ground stands x feet from the billboard. Express θ, the vertical angle subtended by the billboard at her eye, in terms of x. Then find the distance x0 the cow must stand from the billboard to maximize θ.

θ (x) =

Question

Vaughn Whitehead

Mathematics

18 September, 12:52

A rectangular billboard 7 feet in height stands in a field so that its bottom is 12 feet above the ground. A nearsighted cow with eye level at 4 feet above the ground stands x feet from the billboard. Express θ, the vertical angle subtended by the billboard at her eye, in terms of x. Then find the distance x0 the cow must stand from the billboard to maximize θ.

θ (x) =

+4

Answers (1)

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Diana Stewart · Answer 1

We form rectangular triangle. Ninghty degrees angle.

Step-by-step explanation:

1) the top of the billboard is

7+12=19 feet above the ground

2) the eye of the cow is

4 feet high

3) the opposite side of the triangle is

19-4=15 feet

4) the distance between cow eye and billboard is

"x"

5) tg (θ) = 15/x

6) x=15/tg (Θ)